Finite Frequency Regime Research Articles

Charge, spin, and heat shot noises in the absence of average currents: Conditions on bounds at zero and finite frequencies

Nonequilibrium situations where selected currents are suppressed are of interest in fields like thermoelectrics and spintronics, raising the question of how the related noises behave. We study such zero-current charge, spin, and heat noises in a two-terminal mesoscopic conductor. In the presence of voltage, spin, and temperature biases, the nonequilibrium (shot) noises of charge, spin, and heat can be arbitrarily large, even if their average currents vanish. However, as soon as a temperature bias is present, additional equilibrium (thermal-like) noise necessarily occurs. We show that this equilibrium noise sets an upper bound on the zero-current charge and spin shot noises, even if additional voltage or spin biases are present. We demonstrate that these bounds can be overcome for heat transport by breaking the spin and electron-hole symmetries, respectively. By contrast, we show that the bound on the charge noise for strictly two-terminal conductors even extends into the finite-frequency regime.

Sensitivity kernels in seismic wave propagation: a simplified explanation for the banana-doughnut paradox

Ray theory, a high-frequency approximation to describe wave propagation, has been a cornerstone in seismology for over a hundred years. Despite its simplicity and wide range of applications, some limitations combined with the ever-increasing computational power motivated the development of finite-frequency theory, a better model to describe how the Earth’s inner structure affects seismic waves. Finite-frequency theory has matured a lot in the last decades, and it is now widely applied in many geophysical problems. However, most students and even some experienced researchers face difficulties understanding it. An appropriate theoretical comprehension is paramount to making the most out of the methods a theory underpins, avoiding pushing it beyond its limits, and further developing it. With that problem in mind, this paper shows a simplified formulation of the sensitivity kernels, which are the generalization of rays in the finite-frequency regime. The resultant model, despite its limitations, correctly predicts the main features of finite-frequency theory, including the zero sensitivity in the middle of the travel-time kernels, known as the banana-doughnut paradox, shedding new light on that intriguing phenomenon. The step-by-step derivation and relatively easy equations should be understandable by an undergraduate student with a reasonable knowledge of classical physics and calculus. A Colab Notebook implementing the main formulas accompanies the paper, allowing readers to interact and play with the results.

Spectral Properties of Neumann-Poincaré Operator and Anomalous Localized Resonance in Elasticity Beyond Quasi-Static Limit

This paper is concerned with the polariton resonances and their application for cloaking due to anomalous localized resonance (CALR) for the elastic system within finite frequency regime beyond the quasi-static approximation. We first derive the complete spectral system of the Neumann-Poincare operator associated with the elastic system in $\mathbb{R}^{3}$ within the finite frequency regime. Based on the obtained spectral results, we construct a broad class of elastic configurations that can induce polariton resonances beyond the quasi-static limit. As an application, the invisibility cloaking effect is achieved through constructing a class of core-shell-matrix metamaterial structures provided the source is located inside a critical radius. Moreover, if the source is located outside the critical radius, it is proved that there is no resonance.

Nonequilibrium electron relaxation in graphene

We apply memory function formalism to investigate nonequilibrium electron relaxation in graphene. Within the premises of two-temperature model (TTM), explicit expressions of the imaginary part of the memory function or generalized Drude scattering rate (1/[Formula: see text]) are obtained. In the DC limit and in equilibrium case where electron temperature (Te) is equal to phonon temperature (T), we reproduce the known results (i.e., 1/[Formula: see text][Formula: see text]T4 when T[Formula: see text][Formula: see text] and 1/[Formula: see text][Formula: see text]T when T[Formula: see text][Formula: see text], where [Formula: see text] is the Bloch–Grüneisen temperature). We report several new results for 1/[Formula: see text] where T[Formula: see text][Formula: see text][Formula: see text]Te relevant in pump–probe spectroscopic experiments. In the finite-frequency regime we find that 1/[Formula: see text] when [Formula: see text], and for [Formula: see text] it is [Formula: see text]-independent. These results can be verified in a typical pump–probe experimental setting for graphene.

Cloaking via anomalous localized resonance for doubly complementary media in the finite frequency regime

Cloaking a source via anomalous localized resonance (ALR) was discovered by Milton and Nicorovici in [15]. A general setting in which cloaking a source via ALR takes place is the setting of doubly complementary media. This was introduced and studied in [20] for the quasistatic regime. In this paper, we study cloaking a source via ALR for doubly complementary media in the finite frequency regime. To this end, we establish the following results: (1) Cloaking a source via ALR appears if and only if the power blows up; (2) The power blows up if the source is “placed” near the plasmonic structure; (3) The power remains bounded if the source is far away from the plasmonic structure. Concerning the analysis, on one hand we extend ideas from [20] and on the other hand we add new insights into the problem. This allows us to not only overcome difficulties related to the finite frequency regime but to also obtain new information on the problem. In particular, we are able to characterize the behavior of fields far enough from the plasmonic shell, as the loss approaches 0 for an arbitrary source outside the core-shell structure in the doubly complementary media setting.

Analysis of electromagnetic scattering from plasmonic inclusions beyond the quasi-static approximation and applications

This paper is concerned with the analysis of time-harmonic electromagnetic scattering from plasmonic inclusions in the finite frequency regime beyond the quasi-static approximation. The electric permittivity and magnetic permeability in the inclusions are allowed to be negative-valued. Using layer potential techniques for the full Maxwell system, the scattering problem is reformulated into a system of integral equations. We derive the complete eigensystem of the involved matrix-valued integral operator within spherical geometry. As applications, we construct two types of plasmonic structures such that one can induce surface plasmon resonances within finite frequencies and the other one can produce invisibility cloaking. It is particularly noted that the cloaking effect is a newly found phenomenon and is of different nature from those existing ones for plasmonic structures in the literature. The surface plasmon resonance result may find applications in electromagnetic imaging.

On novel elastic structures inducing polariton resonances with finite frequencies and cloaking due to anomalous localized resonances

This paper is concerned with the theoretical study of polariton resonances for linear elasticity governed by the Lamé system in R3, and their application for cloaking due to anomalous localized resonances. We derive a very general and novel class of elastic structures that can induce polariton resonances. It is shown that if either one of the two convexity conditions on the Lamé parameters is broken, then we can construct certain polariton structures that induce resonances. This significantly extends the relevant existing studies in the literature where the violation of both convexity conditions is required. Indeed, the existing polariton structures are a particular case of the general structures constructed in our study. Furthermore, we consider the polariton resonances within the finite frequency regime, and rigorously verify the quasi-static approximation for diametrically small polariton inclusions. Finally, as an application of the newly found structures, we construct a polariton device of the core-shell-matrix form that can induce cloaking due to anomalous localized resonance in the quasi-static regime, which also includes the existing study as a special case.

Dynamical electrical conductivity of graphene

For graphene (a Dirac material) it has been theoretically predicted and experimentally observed that DC resistivity is proportional to T4 when the temperature is much less than Bloch–Grüneisen temperature () and T-linear in the opposite case (). Going beyond this case, we investigate the dynamical electrical conductivity in graphene using the powerful method of the memory function formalism. In the zero frequency regime, we obtain the above mentioned behavior which was previously obtained using the Bloch–Boltzmann kinetic equation. In the finite frequency regime, we obtain several new results: (1) the generalized Drude scattering rate, in the zero temperature limit, shows behavior at low frequencies () and saturates at higher frequencies. We also observed the Holstein mechanism, however, with different power laws from that in the case of metals; (2) at higher frequencies, , and higher temperatures , we observed that the generalized Drude scattering rate is linear in temperature. In addition, several other results are also obtained. With the experimental advancement of this field, these results should be experimentally tested.

Finite frequency Seebeck coefficient of metals: A memory function approach

We study the dynamical thermoelectric transport in metals subjected to the electron-impurity and the electron-phonon interactions using the memory function formalism. We introduce a generalized Drude form for the Seebeck coefficient in terms of thermoelectric memory function and calculate the latter in various temperature and frequency limits. In the zero frequency and high temperature limit, we find that our results are consistent with the experimental findings and with the traditional Boltzmann equation approach. In the low temperature limit, we find that the Seebeck coefficient is quadratic in temperature. In the finite frequency regime, we report new results: In the electron-phonon interaction case, we find that the Seebeck coefficient shows frequency independent behavior both in the high frequency regime (ω⪢ωD, where ωD is the Debye frequency) and in the low frequency regime (ω⪡ωD), whereas in the intermediate frequencies, it is a monotonically increasing function of frequency. In the case of the electron-impurity interaction, first it decays and then after passing through a minimum it increases with the increase in frequency and saturates at high frequencies.

Role of acoustic phonons in frequency dependent electronic thermal conductivity of graphene

We study the effect of the electron–phonon interaction on the finite frequency dependent electronic thermal conductivity of two dimensional graphene. We calculate it for various acoustic phonons present in graphene and characterized by different dispersion relations using the memory function approach. It is found that the electronic thermal conductivity κe(T) in the zero frequency limit follows different power law for the longitudinal/transverse and the flexural acoustic phonons. For the longitudinal/transverse phonons, κe(T)∼T−1 at the low temperature and saturates at the high temperature. These signatures qualitatively agree with the results calculated by solving the Boltzmann equation analytically and numerically. Similarly, for the flexural phonons, we find that κe(T) shows T1/2 law at the low temperature and then saturates at the high temperature. In the finite frequency regime, we observe that the real part of the electronic thermal conductivity, Re[κe(ω,T)] follows ω−2 behavior at the low frequency and becomes frequency independent at the high frequency.

Polarization bandgaps and fluid-like elasticity in fully solid elastic metamaterials.

Elastic waves exhibit rich polarization characteristics absent in acoustic and electromagnetic waves. By designing a solid elastic metamaterial based on three-dimensional anisotropic locally resonant units, here we experimentally demonstrate polarization bandgaps together with exotic properties such as ‘fluid-like' elasticity. We construct elastic rods with unusual vibrational properties, which we denote as ‘meta-rods'. By measuring the vibrational responses under flexural, longitudinal and torsional excitations, we find that each vibration mode can be selectively suppressed. In particular, we observe in a finite frequency regime that all flexural vibrations are forbidden, whereas longitudinal vibration is allowed—a unique property of fluids. In another case, the torsional vibration can be suppressed significantly. The experimental results are well interpreted by band structure analysis, as well as effective media with indefinite mass density and negative moment of inertia. Our work opens an approach to efficiently separate and control elastic waves of different polarizations in fully solid structures.

Anomalous Localized Resonance Phenomena in the Nonmagnetic, Finite-Frequency Regime

The phenomenon of anomalous localized resonance (ALR) is observed at the interface between materials with positive and negative material parameters and is characterized by the fact that when a given source is placed near the interface, the electric and magnetic fields start to have very fast and large oscillations around the interface as the absorption in the materials becomes very small while they remain smooth and regular away from the interface. In this paper, we discuss the phenomenon of anomalous localized resonance (ALR) in the context of an infinite slab of homogeneous, nonmagnetic material (μ=1) with permittivityϵs=-1-iδfor some small lossδ≪1surrounded by positive, nonmagnetic, homogeneous media. We explicitly characterize the limit value of the product between frequency and the width of slab beyond which the ALR phenomenon does not occur and analyze the situation when the phenomenon is observed. In addition, we also construct sources for which the ALR phenomenon never appears.

Cloaking using complementary media for the Helmholtz equation and a three spheres inequality for second order elliptic equations

Cloaking using complementary media was suggested by Lai et al. in 2009. This was proved by H.-M. Nguyen (2015) in the quasistatic regime. One of the difficulties in the study of this problem is the appearance of the localized resonance, i.e., the fields blow up in some regions and remain bounded in some others as the loss goes to 0. To this end, H.-M. Nguyen introduced the technique of removing localized singularity and used a standard three spheres inequality. The method used also works for the Helmholtz equation. However, it requires small size of the cloaked region for large frequency due to the use of the (standard) three spheres inequality. In this paper, we give a proof of cloaking using complementary media in the finite frequency regime without imposing any condition on the cloaked region; the cloak works for an arbitrary fixed frequency provided that the loss is sufficiently small. To successfully apply the above approach of Nguyen, we establish a new three spheres inequality. A modification of the cloaking setting to obtain illusion optics is also discussed.

Dynamic response of silicon nanostructures at finite frequency: An orbital-free density functional theory and non-equilibrium Green's function study

Orbital-free density functional theory (OFDFT) replaces the wavefunction in the kinetic energy by an explicit energy functional and thereby speeds up significantly the calculation of ground state properties of the solid state systems. So far, the application of OFDFT has been centered on closed systems and less attention is paid on the transport properties in open systems. In this paper, we use OFDFT and combine it with non-equilibrium Green's function to simulate equilibrium electronic transport properties in silicon nanostructures from first principles. In particular, we study ac transport properties of a silicon atomic junction consisting of a silicon atomic chain and two monoatomic leads. We have calculated the dynamic conductance of this atomic junction as a function of ac frequency with one to four silicon atoms in the central scattering region. Although the system is transmissive with dc conductance around 4 to 5 e2/h, capacitive-like behavior was found in the finite frequency regime. Our analysis shows that, up to 0.1 THz, this behavior can be characterized by a classic RC circuit consisting of two resistors and a capacitor. One resistor gives rise to dc resistance and the other one accounts for the charge relaxation resistance with magnitude around 0.2 h/e2 when the silicon chain contains two atoms. It was found that the capacitance is around 5 aF for the same system.

Hybrid elastic solids

Metamaterials can exhibit electromagnetic and elastic characteristics beyond those found in nature. In this work, we present a design of elastic metamaterial that exhibits multiple resonances in its building blocks. Band structure calculations show two negative dispersion bands, of which one supports only compressional waves and thereby blurs the distinction between a fluid and a solid over a finite frequency regime, whereas the other displays 'super anisotropy' in which compressional waves and shear waves can propagate only along different directions. Such unusual characteristics, well explained by the effective medium theory, have no comparable analogue in conventional solids and may lead to novel applications.

Energetics of rocked inhomogeneous ratchets.

We study the efficiency of frictional thermal ratchets driven by a finite frequency driving force and in contact with a heat bath. The efficiency exhibits varied behavior with driving frequency. Both nonmonotonic and monotonic behavior have been observed. In particular, the magnitude of the efficiency in the finite frequency regime may be more than the efficiency in the adiabatic regime. This is our central result for rocked ratchets. We also show that for the simple potential we have chosen, with only spatial asymmetry (homogeneous system) or only a frictional ratchet (symmetric potential profile), the adiabatic efficiency is always more than in the nonadiabatic case.